Super Safi’s Monday Morning Math Mayhem 16 – Bat Math Part 4: Earned Run Average

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)


Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

With baseball season officially underway, this month we’re going to explore one of my favourite branches of math – sabermetrics. After all, as Prof Frink so aptly said, “baseball is a game played by the dexterous, but only understood by the poin-dextrous.”



As we discussed three weeks ago, two weeks ago, and last week, Sabermetrics is the empirical analysis of baseball, especially baseball statistics that measure in-game activity. We also mentioned that the term is derived from the acronym SABR, which stands for the Society for American Baseball Research, founded in 1971. The term sabermetrics was coined by Bill James, who is one of its pioneers and is often considered its most prominent advocate and public face. While we discussed the recent work of Bill James two weeks ago and the influence of Branch Rickey last week, this week we return to the pioneer work of Henry Chadwick we first discussed three weeks ago.


Henry Chadwick proposed earned run average as a statistic to evaluate the efficacy of pitchers. However, as most pitchers pitched complete games in that era, wins and losses were the predominant stat used to determine pitching effectiveness. In 1912, the National League was the first to use earned run average, though it was called the “Heydler’s Statistic”, named after then National League (NL) President John Heydler (pictured below). 

(July 10, 1869 – April 18, 1956)

After working as a NL umpire, John Heydler was hired in 1903 as the private secretary to NL president Harry Pulliam, principally working to compile league playing statistics. He was an early advocate for the recording of new statistics, such as runs batted in (RBI) and Chadwick’s earned run average. In 1909, he became President of the National League. In 1912, he implemented Chadwick’s earned run average, known then as the “Heydler’s Statistic”.

Other significant contributions by Heydler include establishing the Baseball Hall of Fame and from a sabermetrics perspective, he hired the Elias brothers as official keeper of playing statistics in 1919. [If any of you have watched any North American professional sports, you must have heard of the Elias Sports Bureau that was founded by the Elias brothers.]

So let’s take a look at “Heydler’s Statistic”, which was later renamed back to earned run average as per the innovator behind the statistic, Henry Chadwick.


Earned Run Average

Earned run average (ERA) is the mean of earned runs given up by a pitcher per nine innings pitched (the traditional length of a game).

ERA  =  [ER Allowed  ÷  IP]  x  9

It is determined by dividing the number of earned runs (ER) allowed by the number of innings pitched (IP) and multiplying by 9 (the traditional length of a game). Runs resulting from defensive errors (including pitchers’ defensive errors) are recorded as unearned runs and are omitted from ERA calculations.

If you look at the leaderboard for all time career ERA leaders, the overwhelming majority are pitchers who pitched before 1920, in what is known as the “Dead-ball era”. Because of rules changes post-1920, most notably the abolition of the spitball and frequent replacement of soiled or scuffed baseballs, the increased importance of the home run (largely due to Babe Ruth), and the American League’s adoption of the designated hitter rule, ERAs have been noticeably higher in the “Live-ball era” post-1920, than in the early decades of the sport.


In The Twisted World of Marge Simpson (Season 08, Episode 11), after getting kicked out of the Springfield Investorettes, Marge invests in a pretzel franchise. But when her new business starts to fail, Homer turns to the mafia in Springfield to help turn Marge’s failing business around.

Marge offers ‘Free Pretzel Day’ at the Springfield Isotopes baseball stadium. Before the crowd has a chance to consume their complimentary pretzels, it is announced that Mr. Burns has won a 1997 Pontiac Astro Wagon in the day’s give-away competition. The fans react angrily to the news and bombard Mr. Burns on the field with the pretzels, knocking out legendary Hall of Famer Whitey Ford in the process.

Bart: “Oh, cheer up, Mom. You can’t buy publicity like that. Thousands and thousands of people saw your pretzels injuring Whitey Ford.
Homer: “You can call them Whitey-Whackers!


Since the “live-ball era” in 1920, the ERA leaderboard amongst pitchers who have pitched at least 1,000 innings includes Hall of Famer Whitey Ford (pictured below) currently in fourth place. [Clayton Kershaw is still pitching and his ERA may change as he gets older.]

  1. Mariano Rivera, NYY 1995-2013, ERA 2.21
  2. Clayton Kershaw, LAD 2008-Active, ERA 2.36
  3. Hoyt Wilhelm, NYM/STL/CLE/BAL/CWS/LAA/ATL/CHC/LAD 1952-1972, ERA 2.52
  4. Whitey Ford, NYY 1950-1967, ERA 2.75

So let’s calculate Whitey Ford’s earned run average:

ERA  =  [ER Allowed  ÷  IP]  x  9  =  [967  ÷  3,170 and 1/3]  x  9  =  0.305  x  9  =  2.75

So Whitey Ford has a career earned run average of 2.75 after allowing 967 earned runs in 3,170 and a third of an inning over his career. That is to say that on average, he allowed 2.75 earned runs allowed for every 9 innings he pitched throughout his career.


As was mentioned last two weeks, in Homer at the Bat (Season 03, Episode 17), we saw Homer’s softball team bring in Roger Clemens. Clemens played two seasons for the Toronto Blue Jays in 1997 and 1998, winning the American League Cy Young award for best pitcher both years. Not only that, both times he pitched for the Triple Crown – leading the American League in wins, strike outs, and earned run average, a feat only accomplished 38 times in both the American and National Leagues.

So let’s calculate Roger Clemens’ earned run average for the 1997 season with the Toronto Blue Jays:

ERA  =  [ER Allowed  ÷  IP]  x  9  =  [60  ÷  264]  x  9  =  0.227  x  9  =  2.05

So Roger Clemens had a season earned run average of 2.05 after allowing just 60 earned runs in 264 innings over the 1997 season. That is to say that on average, he allowed 2.05 earned runs allowed for every 9 innings he pitched throughout that season.


In Bart Has Two Mommies (Season 17, Episode 14), left handed Hall of Fame pitcher Randy Johnson, aka ‘The Big Unit’ makes an appearance as himself intimidating Ned Flanders into buying merchandise to sell in the Leftorium.

So let’s calculate former Montreal Expos draft pick Randy Johnson’s earned run average:

ERA  =  [ER Allowed  ÷  IP]  x  9  =  [1,513  ÷  4,135 and 1/3]  x  9  =  0.366  x  9  =  3.29

So Randy Johnson has a career earned run average of 3.29 after allowing 1,513 earned runs in 4,135 and a third of an inning over his career. That is to say that on average, he allowed 3.29 earned runs allowed for every 9 innings he pitched throughout his career. Though I would be remiss to point out that his career 4,875 strike outs rank second all time to the great Nolan Ryan.


Now that we’ve got a better understanding of earned run average, and calculate the ERA of Simpsons alumni Whitey Ford, Roger Clemens, and Randy Johnson, are you comfortable with the concept? Are you looking forward to seeing this generation of pitchers pitch and what their ERAs will be? Were you already familiar with on-base percentage? Did you remember Whitey Ford appearing in the pretzel episode? Do you remember Homer suggesting they call pretzels Whitey-Whackers? Were you familiar with the live-ball versus dead-ball era differences? Sound off in the comments below. You know we love hearing from you.

2 responses to “Super Safi’s Monday Morning Math Mayhem 16 – Bat Math Part 4: Earned Run Average

  1. Give me ERA+ any day of the week.

  2. It’s funny that I have calculated ERA a little differently, but of course is exactly the same mathematically. I always figure out the number of 9 inning games that a pitcher has pitched and divide the number of earned runs by that number. So I just do ERA=ER÷(IP÷9), which if you keep change flip that you get the formula you presented. Gotta love it!

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